Active questions tagged elasticity - Economics Stack Exchange most recent 30 from economics.stackexchange.com 2019-07-19T15:41:50Z https://economics.stackexchange.com/feeds/tag/elasticity http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://economics.stackexchange.com/q/30218 0 Help with CES utility maximization and elasticies bsb0719 https://economics.stackexchange.com/users/23734 2019-07-19T10:49:45Z 2019-07-19T10:49:45Z <p>I'm trying to solve a utility maximization problem and calculate elasticities in Borjas (1992)'s paper ("Ethnic capital and intergenerational mobility") through the Lagrange method(Equation (1) to (6) are in Borjas (1992)'s paper).</p> <p><em>The utility function is like</em> </p> <p><span class="math-container">$U(k_{t+1},C_t )=[δ_1 k_{t+1}^ρ+δ_2 C_t^ρ]^{1/ρ}$</span> (1)</p> <p><em>Where <span class="math-container">$ρ&lt;1$</span>,and <span class="math-container">$σ=1/(1-ρ)$</span> is the elasticity of substitution between <span class="math-container">$C_t$</span> and <span class="math-container">$k_{t+1}$</span>.</em></p> <p><em>The person can either sell his <span class="math-container">$k_t$</span> to the market or devote a fraction <span class="math-container">$s_t$</span> of his time to the production the <span class="math-container">$k_{t+1}$</span>. Setting the price of <span class="math-container">$C_t$</span> as the numaraire implies that</em></p> <p><span class="math-container">$R(1-s_t ) k_t=C_t$</span> (2)</p> <p><em>And the production function for <span class="math-container">$k_{t+1}$</span> is like</em></p> <p><span class="math-container">$k_{t+1}=β_0 (s_t k_t )^{β_1} k̅_t^{β_2}$</span> (3)</p> <p><em>The maximization of (1) subject to the budget constraint and the production technology, generate the household's supply function for time allocated to investing in <span class="math-container">$k_{t+1}$</span>:</em></p> <p><span class="math-container">$s_t=(k_t,k̅_t)$</span> (4)</p> <p><strong>I have two questions.</strong></p> <p>First, for the maximization of Utility function, i made a equation like:</p> <p><span class="math-container">$L=U(k_{t+1},C_t )=[δ_1 k_{t+1}^ρ+δ_2 C_t^ρ]^{1/ρ}+λ_1(C_t-R(1-s_t ) k_t)+λ_2(k_{t+1}-β_0 (s_t k_t )^{β_1} k̅_t^{β_2}+λ_3(1-(1-s_t)-s_t)$</span> </p> <p>is it correct? </p> <p>Second, in the paper the elasticities of <span class="math-container">$s_t$</span> with respect to <span class="math-container">$k_t$</span> and <span class="math-container">$k̅_t$</span> are show:</p> <p><span class="math-container">$(∂logs_t)/(∂logk_t )=ρ(β_1-1)(1-s_t )/((1-s_t )(1-ρβ_1 )+s_t (1-ρ) )$</span> (5)</p> <p><span class="math-container">$(∂logs_t)/(∂logk ̅_t )=(ρβ_2 (1-s_t ))/((1-s_t )(1-ρβ_1 )+s_t (1-ρ) )$</span> (6)</p> <p>How i get these elasticites? Do i must find the functions <span class="math-container">$s_t$</span>, <span class="math-container">$k_t$</span>, and <span class="math-container">$k ̅_t$</span> through the maximization of CES utility function?</p> <p>Any help would be appreciated.</p> https://economics.stackexchange.com/q/30139 0 How to simulate changes in quantity demanded when several prices change? ninapatari https://economics.stackexchange.com/users/23684 2019-07-12T11:56:06Z 2019-07-12T11:56:06Z <p>I am not sure if this is a straightforward question or not. Basically, I have a set of products along with their prices and quantities demanded. I also have own and cross price elasticities for each product as well as the cross price elasticity with my outside good. I want to figure out how quantity demanded will change when the prices of several products changes. For example, if my products are different types of beers and the outside option is wine, I want to know how quantity demanded of all beers and wine will change when several beers change their price. I want to assume that total quantity demanded of beer and wine remain constant (but expenditure can increase). Finally, I do not want to estimate a demand model I just want to use the elasticities that I already have access to (from an outside source).</p> https://economics.stackexchange.com/q/26340 0 Monthly price elasticity and possibility of using daily values axel2020 https://economics.stackexchange.com/users/20710 2019-01-09T10:26:40Z 2019-07-11T01:01:20Z <p>I am calculating the price elasticity as a starting point to find a theoretical optimal price that would maximize our revenue.<br> I am looking at <strong>2 years data</strong> and to use the price elasticity formula, I am considering <strong>monthly values separately</strong> <em>(this also because given the strong seasonality we have, i would expect different elasticity per month and I would like to suggest different prices every month).</em> </p> <p>To get the <strong>monthly Price Elasticity</strong>, I calculate for each month Prices and Quantities of the respective year: </p> <p><span class="math-container">$$\frac{(Q^{2018} - Q^{2017})/Q^{2017}}{(P^{2018} - P^{2017})/P^{2017}}$$</span></p> <p><strong>Question 1:</strong> Is this correct? Using aggregated monthly data is enough? What if I had also 2016 data? How could I put this extra information in the formula? </p> <p><strong>Question 2:</strong> Could I use daily data to calculate the price elasticity? Could I plot 2 years data and use the linear trend line for the elasticity calculation? </p> <p>Thanks in advance, any help is highly appreciated!</p> https://economics.stackexchange.com/q/30119 0 Effect of a change in quality on price elasticity of demand user444152 https://economics.stackexchange.com/users/23661 2019-07-10T15:12:19Z 2019-07-10T18:32:13Z <p>I am interested to know how one would expect a change in the quality of a product to affect its price elasticity of demand. Two example will illustrate my confusion:</p> <p><strong>Example 1</strong></p> <p>Suppose a producer is selling tap water at price P with quantity demanded Q. Let us call this good 'Beverage v1'. The producer changes the recipe; adding some grape juice and carbon dioxide to make Champagne. The producer continues to sell at price P but now with demand Q2>Q (in the short-run, which is probably not an equilibrium). Let us call this good 'Beverage v2'.</p> <p>We would, I think, expect the price elasticity of demand for Beverage v2 to be lower than that of Beverage v1. The common intuition is that 'essential' goods have lower PEoD than 'luxury' goods.</p> <p><strong>Example 2</strong></p> <p>Now suppose a producer is selling a medicine ('Medicine v1') which treats the symptoms of an illness pretty well. It is the only medicine for this illness so patients must choose between going untreated (feeling pretty awful) and buying the drug, which makes them feel 50% better than going untreated. The medicine is sold at price P with quantity demanded Q. The producer then makes some changes and now the medicine makes patients feel 100% better. It is not quite a cure, as patients have to keep taking the medicine, but it is pretty close. Let us call this 'Medicine v2'. The producer continues to sell at price P but now with quantity demanded Q2>Q (in the short-run, which is probably not an equilibrium). Bear in mind that Medicine v1 is no longer available and that there are no other alternatives available either (except going untreated).</p> <p>This seems to be similar to the beverage example above, but I feel as if the intuition is less clear in this case that PEoD for Medicine v2 would be higher than for Medicine v1. Is feeling 100% better more of a luxury than feeling 50% better? It is certainly better, but I am not certain that is therefore less essential. What do you think?</p> https://economics.stackexchange.com/q/30041 2 Why is elasticity not constant on a straight line graph? fyiitsme https://economics.stackexchange.com/users/23596 2019-07-04T00:41:23Z 2019-07-04T09:08:58Z <p>There are different zones of elasticity on a graph, but if we are to imagine a negatively sloped, straight line on a price v quantity graph, we find that elasticity differs based on where we look on the graph. Why is this the case, rather then elasticity being constant?</p> https://economics.stackexchange.com/q/16895 0 Price optimization with demand forecast Abhishek Singh https://economics.stackexchange.com/users/13360 2017-05-24T17:53:47Z 2019-07-03T00:02:20Z <p>I have one year sales data of a retail company and lets say I am forecasting the next month sales for the product. I have got the sales using time series in R. Now I want to forecast the price as well. I want to build a model using both the demand and price. My function should be <strong>f(D<em>P)</strong> where D is demand and P is price. I want to maximize Revenue or Profit where <strong>Revenue=D</em>P</strong>.</p> <p>As of now, I forecasted sales and did a linear programming on Price itself to get optimal price of a single product. I want my model to be robust but this is chicken - egg theory where demand forecast is dependent on the price and price is dependent on demand. Please help by sharing some theories which would better fit for this or some R models.</p> https://economics.stackexchange.com/q/29954 0 Constant elasticity proof for log-linear demand curve huppuguga https://economics.stackexchange.com/users/23539 2019-06-25T20:59:02Z 2019-06-25T21:28:08Z <p>From Perloff 2008e solved 2.2:</p> <p>Q: Show that the elasticity of demand is a constant e if the demand function is log-linear, ln Q=ln A+e ln p. A: Differentiating with respect to p, we find that (dQ/dp)/Q=e/p.</p> <p>Where did 'dQ/dp' come from in the numerator? </p> https://economics.stackexchange.com/q/29793 0 Should a Price Elasticity of Demand model exclude items that sold out or marked down from the original price qwerty https://economics.stackexchange.com/users/23430 2019-06-14T21:10:51Z 2019-06-17T05:21:25Z <p>Consider a Price Elasticity of Demand model built with linear regression to estimate the Percent Change in Quantity Demanded given a Percent Change in Price specifically for specialty items which have a selling period of only a few weeks in all stores. </p> <p>Data is aggregated based on shared item "Categories" (eg both winter coats and swim trunks are considered Clothing), each store's total sales units for the item's selling period is known rather than daily sales, items that sellout at a store will not be replenished, the demand curve is convex, and elasticity is constant along the curve. </p> <p><span class="math-container">$$Q=aP^{-b}\\ E=(dQ/dP)*P/Q\\ E=-abP^{(-b-1)}*(P/Q)\\ E=b\\$$</span> Because I'm using the log-log form of linear regression, the slope coefficient of the model is the estimated elasticity. If a store sells out of an item before the end of the item's selling period, I think it would result in a more positive slope coefficient and appear more inelastic than actual. If a store marks down the price of an item before the end of the item's selling period, I think it would result in a more negative slope coefficient and appear more elastic than actual.</p> <p>If an item is sold out at one store or if its price is marked down during its shelf-life should the item be excluded from the data set for that particular store? If the data is removed, how would elasticity be affected?</p> https://economics.stackexchange.com/q/29696 1 How do you use a Log-linear model when you have negative Xs? Maddy https://economics.stackexchange.com/users/23363 2019-06-07T09:51:58Z 2019-06-07T15:02:59Z <p>I am trying to us a Log-linear model to derive an elasticity. However, some of my Xs are negative numbers. Being as the model relies on the natural log of the Ys and the Xs, how can this model work when the natural log can only be taken of X>0? </p> https://economics.stackexchange.com/q/8892 2 Elasticity with perfectly inelastic / elastic demand GoodChessPlayer https://economics.stackexchange.com/users/5969 2015-10-26T10:33:30Z 2019-05-23T17:46:45Z <p>When a change in price results in an infinitely large response in quantity demanded, demand is perfectly elastic. The perfectly elastic demand curve is horizontal. At price P, consumers will buy a quantity Q. If there is an increase in price, quantity demanded drops to zero due to the existence of perfect substitutes. However, when price drops, how will the PED remain infinity? Wouldn't consumers demand as much, if not more, of the product?</p> https://economics.stackexchange.com/q/29344 0 Engel’s Coefficient Data SDH https://economics.stackexchange.com/users/21520 2019-05-15T20:57:38Z 2019-05-16T17:58:45Z <p>Does anyone know of any good data sources where we can find Engel’s Coefficients by nation?</p> https://economics.stackexchange.com/q/29297 1 If $X$ is a Giffen good then $Y$ must be a normal good Vizag https://economics.stackexchange.com/users/21361 2019-05-12T21:57:03Z 2019-05-15T13:34:10Z <p>While going through some problems as part of self-study I encountered the following True/False question: </p> <p>Q. Steven only consumes two goods: <span class="math-container">$X$</span> and <span class="math-container">$Y$</span>. If <span class="math-container">$X$</span> is a Giffen good for Steven, then <span class="math-container">$Y$</span> must be a normal good for Steven.</p> <p>The given answer is True.</p> <p>I am unable to understand why it is necessary for the other good to be normal. Why can't it be inferior/Giffen?</p> https://economics.stackexchange.com/q/29047 0 Homogeneity in Marshallian demand function 6.19 https://economics.stackexchange.com/users/20278 2019-04-30T19:26:11Z 2019-04-30T19:26:11Z <p><a href="https://i.stack.imgur.com/bzaeU.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/bzaeU.png" alt="enter image description here"></a></p> <p>I have worked out the expenditure function for a Marshallian demand function, R represents a fixed cost and the questions asks about why the expenditure function is unusual.</p> <p>The answer explains it is due to the fact that the two prices do not have a homogenous degree of 1 due to the fixed cost R. But I don't get why p1 and p2 need to have a homogenous degree of 1- what is the implication of this?</p> <p>Thanks</p> https://economics.stackexchange.com/q/29034 2 How does one do a hypothesis test for elasticity? ahorn https://economics.stackexchange.com/users/175 2019-04-29T16:53:25Z 2019-04-29T20:21:42Z <blockquote> <p>Given the regression output <span class="math-container">$$\widehat{\ln cons} = \underset{(0.6018)}{0.4054} + \underset{(0.0744)}{1.2739}\, \ln m - \underset{(0.1902)}{0.6666}\, \ln p_1 -\underset{(0.2645)}{1.6146}\, \ln p_2$$</span> where </p> <ul> <li><span class="math-container">$\ln cons$</span> is the log of chocolate consumption,</li> <li><span class="math-container">$\ln m$</span> is the log of income,</li> <li><span class="math-container">$\ln p_1$</span> is the log of the price of chocolate, and</li> <li><span class="math-container">$\ln p_2$</span> is the log of the price of sweets,</li> </ul> <p>test whether chocolate is a luxury good.</p> </blockquote> <p>Since <span class="math-container">$1.27 &gt; 1$</span>, it is logical to test whether <span class="math-container">$\beta_{\ln m}$</span> could be less than <span class="math-container">$1$</span>. When I test elasticity, I base the null hypothesis on what is logical, as in this case if <span class="math-container">$\beta_{\ln m}$</span> is significantly greater than <span class="math-container">$1$</span>, one shouldn't reject a (illogical) null hypothesis <span class="math-container">$\mathrm H_0: \beta_{\ln m} \geq 1$</span>. So,</p> <p><span class="math-container">$\mathrm H_0: \beta_{\ln m} \leq 1$</span></p> <p><span class="math-container">$\mathrm H_1: \beta_{\ln m} &gt; 1$</span></p> <p><span class="math-container">$\displaystyle t = \frac{1.2739-1}{0.0744}\approx 3.681$</span></p> <p>Therefore, I reject the null hypothesis in favour of the alternative that chocolates are a luxury good.</p> <p>Do you agree with the way I have set up this hypothesis test? If the estimate were less than 1, I would have stated <span class="math-container">$\mathrm H_0: \beta_{\ln m} \geq 1$</span> against the alternative <span class="math-container">$\mathrm H_1: \beta_{\ln m} &lt; 1$</span>.</p> https://economics.stackexchange.com/q/29029 1 Can there be a good which has both Hicksian and Marshallian demand curves vertical? PGupta https://economics.stackexchange.com/users/18507 2019-04-29T07:28:39Z 2019-04-29T07:28:39Z <p>Consider a perfectly inelastic (Marshallian) demand curve for a good X. Does this good also have a vertical Hicksian demand curve?</p> https://economics.stackexchange.com/q/28969 0 Unitary Elasticity Of Demand Question (PED=1) [duplicate] econnewbie https://economics.stackexchange.com/users/22945 2019-04-24T17:52:27Z 2019-04-24T17:52:27Z <div class="question-status question-originals-of-duplicate"> <p>This question already has an answer here:</p> <ul> <li> <a href="/questions/10691/elasticity-of-demand-equals-1-but-income-decreases" dir="ltr">Elasticity of demand equals -1 but income decreases!</a> <span class="question-originals-answer-count"> 2 answers </span> </li> </ul> </div> <p>So I was having a bit of trouble reasoning with the answer for this particular PED question. It goes like this:</p> <p><strong>PED=1</strong>, <strong>Quantity Demanded=4,000 units when Price=$12</strong></p> <p>The question was:</p> <p><strong>Find the price when Quantity Demanded=20,000 units</strong></p> <p>So I tried the easy way to do this which was to use the price in which the Total Revenue remained the same, and I got the answer Final Price=$2.4.</p> <p>My problem was that I tried another method and I am not getting the answer and I want to know why .</p> <p>So PED= <strong>% Change in QD/ % Change in Price</strong></p> <p>We can see that the increase in Quantity Demanded is 400%. Shouldn't it stand to reason that the decrease in Price is also 400% (I know this is impossible because a price can't fall by more than what it is at the moment) but isn't the theory that the % fall in price will equal to and be offset by the % increase in QD, resulting in the revenue remaining the same?</p> <p>I'm sorry if this question was unnecessarily long or even confusing, it's a bit difficult to understand my own thoughts so writing them out in paragraphs helps me understand why I'm asking this question in the first place ;).</p> https://economics.stackexchange.com/q/27928 2 Calculating Price Elasticity of Demand Hiru https://economics.stackexchange.com/users/20901 2019-04-22T12:03:25Z 2019-04-22T17:37:10Z <p>Hi I was given the following price vs quantity values.</p> <pre><code>Price Quantity Demanded 4 221 5 210 6 185 7 162 8 144 9 122 10 102 11 81 12 61 13 46 14 25 </code></pre> <p>The graph was plotted as shown below.</p> <p><a href="https://i.stack.imgur.com/8NqLH.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/8NqLH.png" alt="enter image description here"></a></p> <p>The equation was, <span class="math-container">$Y = -0.0496 X + 15.133$</span>. What I need to know is, I was asked to find the PED when price is <span class="math-container">$\$7.5$</span>.</p> <p>Then what I did was, I found the quantity at price <span class="math-container">$7.5$</span> substituting to the price quantity equation. And then found the PED using the equation</p> <p><a href="https://i.stack.imgur.com/M4YQv.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/M4YQv.png" alt="enter image description here"></a></p> <p>The quantity derived for price <span class="math-container">$7.5$</span> was <span class="math-container">$153.89$</span>. Then I calculated the PED as below. Is it correct?</p> <p><span class="math-container">$$\frac{(153.89-144)/144}{(7.5-8)/8} = 1.099$$</span></p> <p>May I know whether this calculation is correct?</p> https://economics.stackexchange.com/q/19409 2 CES production function application problem macro123 https://economics.stackexchange.com/users/13030 2017-11-21T02:08:11Z 2019-04-17T03:04:10Z <p>I'm currently trying to do some estimations using the micEconCES package in R by Henningsen/Henningsen (2011). My issue is that I am not very familiar with R and I'm trying to implement my own dataset to get the estimations with the package. They authors of the paper created this data set for the estimations. </p> <pre><code>R&gt; set.seed( 123 ) R&gt; cesData &lt;- data.frame(x1 = rchisq(200, 10), x2 = rchisq(200, 10), x3 = rchisq(200, 10), x4 = rchisq(200, 10) ) R&gt; cesData$y2 &lt;- cesCalc( xNames = c( "x1", "x2" ), data = cesData, + coef = c( gamma = 1, delta = 0.6, rho = 0.5, nu = 1.1 ) ) R&gt; cesData$y2 &lt;- cesData$y2 + 2.5 * rnorm( 200 ) R&gt; cesData$y3 &lt;- cesCalc(xNames = c("x1", "x2", "x3"), data = cesData, coef = c( gamma = 1, delta_1 = 0.7, delta = 0.6, rho_1 = 0.3, rho = 0.5, + nu = 1.1), nested = TRUE ) R&gt; cesData$y3 &lt;- cesData$y3 + 1.5 * rnorm(200) R&gt; cesData$y4 &lt;- cesCalc(xNames = c("x1", "x2", "x3", "x4"), data = cesData, coef = c(gamma = 1, delta_1 = 0.7, delta_2 = 0.6, delta = 0.5, rho_1 = 0.3, rho_2 = 0.4, rho = 0.5, nu = 1.1), nested = TRUE ) R&gt; cesData$y4 &lt;- cesData$y4 + 1.5 * rnorm(200) </code></pre> <p>The ﬁrst line sets the“seed”for the random number generator so that these examples can be replicated with exactly the same data set. The second line creates a data set with four input variables (called x1, x2, x3, and x4) that each have 200 observations and are generated from random χ2 distributions with 10 degrees of freedom. The third, ﬁfth, and seventh commands use the function cesCalc, which is included in the micEconCES package, to calculate the deterministic output variables for the CES functions with two, three, and four inputs (called y2, y3, and y4, respectively) given a CES production function. Now in my paper I'm trying to estimate the CES function for the U.S. at the Aggregate Level for the two input case with capital and labor. So what I did is I gathered data from the World Bank Data Base from 1990-2015, where I used Gross Fixed Capital Formation for capital and total Labor Force for Labor.</p> <p>The authors did f.e. a non linear estimation the following way</p> <pre><code>R&gt; cesNls &lt;- nls( y2 ~ gamma * ( delta * x1^(-rho) + (1 - delta) * x2^(-rho) )^(-phi / rho), + data = cesData, start = c( gamma = 0.5, delta = 0.5, rho = 0.25, phi = 1 ) ) R&gt; print( cesNls ) </code></pre> <p>Now I want the exact same thing for my own data Set which is called Data_Extract_From_World_Development_Indicators. So what I did is firstly</p> <pre><code>R&gt; ceslan &lt;- cesCalc( xNames = c( "GrossFixedCapitalFormation", "LaborForce" ), data = Data_Extract_From_World_Development_Indicators, coef = c( gamma = 1, delta = 0.6, rho = 0.5, nu = 1.1 ) ) </code></pre> <p>So i replicated</p> <pre><code>R&gt; cesData$y2 &lt;- cesCalc( xNames = c( "x1", "x2" ), data = cesData, coef = c( gamma = 1, delta = 0.6, rho = 0.5, nu = 1.1 ) ) </code></pre> <p>All I did was changing the name of the Dataset and replaced x1 and x2 with my two variables for capital and Labor.</p> <p>Afterwards I tried to do the non linear estimation</p> <pre><code>R&gt; cesulan &lt;- nls(y2 ~ gamma * (delta * GrossFixedCapitalFormation^(-rho) + (1-delta)*LaborForce^(-rho))^(-phi / rho), data = Data_Extract_From_World_Development_Indicators, start = c(gamma = 0.5, delta = 0.5, rho = 0.25, phi = 1) ) </code></pre> <p>Now this is where my Problem is: I dont know what variable is meant to be y2 in my dataset. I can see in the formula that y2 ~ gamma *... so ist plotted against the rest of the term, but I dont know what Kind of value I need to plug in there. Does anyone have any advice?</p> https://economics.stackexchange.com/q/21587 2 CES function estimation macro123 https://economics.stackexchange.com/users/13030 2018-04-20T13:28:01Z 2019-04-16T00:03:05Z <p>For a paper I was using the micEconCES package to estimate the CES production function for a country at the aggregate. For a two-input function with capital and labour I used for the variables the Perpetual Inventory Method to construct aggregate capital, labour hours and GDP for output. I used methods provided in the package to do the estimation. But now I am kind of unsure, what I have to check the data for f.e. autocorrelation, multicollinearity etc. or do I even have to check for that?</p> https://economics.stackexchange.com/q/27445 3 Elasticity when the demand function is given WorldGov https://economics.stackexchange.com/users/6486 2019-03-25T08:21:48Z 2019-04-07T00:33:56Z <p>Given the demand function, <span class="math-container">$ q = kp^{-\epsilon} $</span>, how do I calculate the elasticity? As a result, I do know that the elasticity when the demand function is in this form is <span class="math-container">$ - \epsilon $</span>. But I'd like to know how. I also found a derivation online that proceeded like this:</p> <p>(1) Take logarithm on both sides (2) Differentiate on boths ides (3) You'll get: <span class="math-container">$$\frac {\text{d} \ln(q)}{\text{d} \ln (p)} = - \epsilon$$</span> (4) The LHS of the above equation is simply elasticity. </p> <p>How does <span class="math-container">$$\frac {\text{d} \ln(q)}{\text{d} \ln (p)}$$</span> represent elasticity?</p> https://economics.stackexchange.com/q/11793 5 Estimating elasticity of substitution in nested CES functions london https://economics.stackexchange.com/users/6009 2016-05-01T11:41:33Z 2019-03-27T01:15:55Z <p>I have aggregate data on$L_t, K_t$and$X_t$, and want to estimate elasticity of substitution parameters,$\gamma$and$\sigma$for these factors. Assuming the production function takes the following form: $$Y_t=(A_lL^{\gamma}+[A_kK_t^{\sigma} +A_xX_t^{\sigma}]^\frac{\gamma}{\sigma})^{\frac{1}{\gamma}}$$</p> <p>Technology parameters,$A$s are not observable and hence need to be controlled for in an econometric specification. I am thinking of first estimating the parameter,$\sigma$, on the inner CES function combining$K$and$X$. Then I should be able to estimate the outer CES parameter,$\gamma$. In a way, the two parameters are not jointly estimated. Would this method be valid, I mean, in statistical sense? Will I get consistent and unbiased estimates? I've read papers on non-linear regression methods, but was wondering if this simple approach is feasible. Thanks.</p> https://economics.stackexchange.com/q/27431 0 How to calculate Store/Category level Price elasticity? user6334582 https://economics.stackexchange.com/users/21600 2019-03-24T07:39:53Z 2019-03-24T07:39:53Z <p>I would like to compare different retail stores at category level using <strong>the percentage change in the category volume produced by a uniform 1% increase in the prices of all items in the category</strong>. What would be the best way to capture that? </p> <p>I have sales data at week level for every item in the category.</p> https://economics.stackexchange.com/q/27357 0 How to Calculate Price Elasticity of Demand When Perfectly Elastic? econguy https://economics.stackexchange.com/users/12859 2019-03-20T04:14:50Z 2019-03-20T23:49:58Z <p>When we have perfect elasticity, the demand curve is a horizontal line and the elasticity of demand coefficient is equal to infinity.</p> <p>How do we arrive at a solution equal to infinity?</p> <p>We know that </p> <blockquote> <p>Elasticity of Demand Coefficient = Change in Quantity Demanded / Change in Price <span class="math-container">$x$</span></p> </blockquote> <p>If we change price by <span class="math-container">$x$</span>, how do we get what the change in quantity demanded is if there is no quantity demanded at the new price?</p> https://economics.stackexchange.com/q/26871 2 What's an example of a resource, raw material that has become scarce? Paul Boosz https://economics.stackexchange.com/users/21089 2019-02-13T09:50:04Z 2019-03-17T20:01:35Z <p>I'm interested in the elasticity price demand that predicts that as a resource becomes more scarce, it gets more expensive. </p> <p>Regarding oil price this isn't clear. Is there an example of a resource that has nearly disappeared ? What was the evolution of its price ?</p> https://economics.stackexchange.com/q/27279 0 Exploratory analysis about elasticity user38642 https://economics.stackexchange.com/users/21390 2019-03-15T14:49:18Z 2019-03-15T15:15:39Z <p>I have been asked to perform some studies about the price elasticity of demand of an online seller. </p> <p>The concept of elasticity used by economists are more clear to me after some research on specialized literature but there is a lacking some clearing about the following subjects:</p> <ul> <li><p>in order to have a clear measurement of the relationship between price and quantity, that prices should be deflated. I believe the economic inflation affects any elasticity measure</p></li> <li><p>There are a clear seasonal effect in the sold quantities and executed prices. This effect must to be addressed or any assessment will be clearly affected...</p></li> </ul> <p>Does it make sense? Someone can recommend any literature/paper where such topics are discussed?</p> https://economics.stackexchange.com/q/27059 0 Elasticity of employment in respect of reduction of working time Elen https://economics.stackexchange.com/users/21242 2019-02-27T23:28:57Z 2019-02-28T03:47:02Z <p>If elasticity of employment in respect to working hours is positive then work time reduction decreases employment and the opposite is true if elasticity is negative? I mean if I want to see how employment increases or decreases by reducing working time and spot an elasticity of a positive number that means that the working time reduction, reduced employment? And equally if the elasticity is negative number the working time reduction increased employment? </p> https://economics.stackexchange.com/q/27000 0 Calculating Demand curve function from Elasticity of demand, price per quantity and quantity purchased? Ethan Hall https://economics.stackexchange.com/users/21198 2019-02-22T18:26:10Z 2019-02-22T18:26:10Z <p>For an assignment I have to model the demand function and find consumer surplus based upon elasticity of demand, price per quantity and quantity purchased. Ill copy and paste the assignment below and then show what I did, but im not quite sure if its correct.</p> <ol> <li>Given the following information, find the linear demand-curve functions for each product. Given the information, what is consumer surplus for each product?</li> </ol> <p>A. Apples: price elasticity of demand is -0.58; price per pound is$1.00; quantity purchased 9.8 million pounds.</p> <p>B. Donuts: price elasticity of demand is -1.70; $2.80 per pound; quantity purchased is 1.3 billion pounds.</p> <p>Here are my solutions, ill explain them below <a href="https://i.stack.imgur.com/scVxy.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/scVxy.jpg" alt="enter image description here"></a></p> <p>for Part A, because the price per quantity is 1:1, i said that the price elasticity of demand is equal to the slope of the line. Is this a correct assumption? from there I wrote the equation in point slope form, did some algebra to make it slope intercept form, which gave the the y intercept so I can calculate the consumer surplus.</p> <p>For part B, since the relationship is not 1:1, and price elasticity of demand is in terms of percentage, I divided the elasticity of demand by the price per unit, effectively showing the relationship between P and Q as if one unit was$1, and then I got my slope. Is this correct? can I do this? From there I followed the same method to find the equation of the line and therefore calculate consumer surplus.</p> <p>So am I doing this correctly? If not how do I go about starting this? Thank you! </p> https://economics.stackexchange.com/q/26888 0 Demand Curve Price not perfectly elastic John Kelly https://economics.stackexchange.com/users/21107 2019-02-14T14:48:24Z 2019-02-15T19:38:07Z <p>I'm trying to make the argument that our Sales go up when prices for all our Products are 30% off. Which I believe should be our new Regular Price. but our Demand Curve doesn't support this. Should I be setting up the demand curve differently? on a per product basis? or package size?</p> <ul> <li><p>I sell our food product in different package sizes 2oz, 4oz, 9oz , 16oz 3.5lb</p></li> <li><p>Normalized the time our products were at that price. </p></li> </ul> <p><a href="https://i.stack.imgur.com/RQQCA.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/RQQCA.png" alt="Demand Curve"></a></p> https://economics.stackexchange.com/q/26876 0 Increase of price of good and effect on elasticity of demand FabolousPotato https://economics.stackexchange.com/users/21095 2019-02-13T16:49:09Z 2019-02-13T16:49:09Z <p>Price elasticity of demand of good A is 1.20. If we increase a price by 15% what will happen to quantity demanded of good A?</p> <p>My answer is 18% increase since % change in Q = 1.20 * %change P Is this a correct reasoning ?</p> https://economics.stackexchange.com/q/26678 0 Should Company B enter the market in the following cases MinaThuma https://economics.stackexchange.com/users/20912 2019-01-30T20:42:09Z 2019-02-03T15:09:13Z <p>Say Company A has a monopoly producing product E, at a constant marginal cost of <span class="math-container">$3$</span> USD. Say the ideal number of units produced is <span class="math-container">$1$</span> unit which produces a profit of <span class="math-container">$2$</span> USD (=<span class="math-container">$P_{A}$</span>). </p> <p>Next, Company B wants to enter the market and produce product E at a marginal cost <span class="math-container">$3$</span> USD, but it has initially invested <span class="math-container">$\frac{1}{2}P_{A}$</span> in order to enter the market. </p> <p><strong>Question:</strong></p> <p><span class="math-container">$1.$</span> Under Cournot Competition, should Company B enter the market. Why/Why not?</p> <p><span class="math-container">$2.$</span> Under Bertrand Competition, should Company B enter the market. Why/Why not?</p> <p>Ideas: </p> <p><span class="math-container">$1.$</span> No, since we are in Cournot competition, the price is determined by the total units that both Company A &amp; B produce together. If Company B were also to produce, it would drive the price down as a result of excess supply, eventually forcing the price below the marginal cost, thus not profitable</p> <p><span class="math-container">$2.$</span> Yes, the price is driven down until the marginal cost. Although Company B will earn <span class="math-container">$\frac{1}{2}P_{A}$</span> less than company A.</p> <p>Do my answers suffice, or rather, are they correct, and touch on the right point? </p>